Term Paper Thesis Argumentation 200 Grade Points
Due As Assigned Via E-mail
Guidelines on Writing a Philosophy Paper:
Start by reading the Notre Dame University Guidelines
http://www.jimpryor.net/teaching/guidelines/writing.html
By Professor Jim Pryor
and finally, Professor Peter Horban's "Writing a Philosophy Paper"
http://www.sfu.ca/philosophy/resources/writing.html
Then, follow these Ten Commandments and everalsting grade salvation shall be thine.
While the primary intent for publishing these 'commandments' is to aid your success in my Logic and
Critical Thinking courses, anyone can use these steps to formulate a defensable term paper in philosophy.
These are NOT mere guidelines for this Critical Thinking and Writing course, however. These are the
NECESSARY AND SUFFICIENT CONDITIONS for writing a successful term paper in this course. Since
satisfying these necessary and sufficient conditions entails demonstrating the skills of VALID and SOUND
reasoning, then many students may well find these 'commandments' useful and productive in writing any
paper assigned in your academic life. Be well and prosperous!
PART ONE OF YOUR TERM PAPER: VALIDITY
1. THOU SHALT STATE THY THESIS: A philosophy paper begins with the statement of a claim to be
defended. This claim is a proposition and constitutes the THESIS of your term paper. The first paragraph of
your paper should state clearly what 'thesis' proposition you intend to defend.
Example: "Political Science is an oxymoron"
Choose a topic from your major academic discipline of study. The example is suitable for a political science
major. If you don’t have a major yet, then choose a claim you wish to defend in an area of study interesting
to you and where you have sufficient general background knowledge.
Example: "There is a high degree of probability that intelligent life exists on other planets in the known
universe."
Perhaps you want to challenge the views of another thinker. If so, then your thesis statement would read
something like this.
Example: "I oppose the view held by Gilbert Ryle that states that the term ‘mind’ refers merely to the
functions of the brain rather than to some being separate from the brain."
Your statement of the claim is your thesis. You will defend this view by advancing a series of reasons called
arguments. You may need many sub-arguments in order to get to your main thesis argument.
Prepare a bulleted outline of what those arguments will entail. List the kinds of evidence or proof you will
need for each argument. Is your argument purely analytical (a priori) like Anselm’s argument for the
existence of God? Then you will have no soundness issues to deal with only issues of validity. Or, is your
argument concerning some area of practical reasoning (a posteriori) as is in the first example stated above
about political science? In that case you will have to deal with both issues of validity and soundness. This
outline should be free from mere opinions, beliefs, feelings, hearsay or things you vaguely remember
Monica Lewinsky saying in her interview with Barbara Walters on TV. Your outline should ONLY
CONTAIN REASONS that support other statements in the outline by logical entailment.
2. THOU SHALT DEFINE ALL THY TERMS: Take each section of your outline and break it down into
smaller sections containing premise statements (propositions) that lead to conclusions. List what kind of
definitions you intend to employ for the terms in the premises you use for each sub-argument and your
main argument. Are your definitions stipulative, lexical, functional, theoretical or some combination
thereof? Make careful note of this in your outline. At this stage, be prepared to go through several drafts of
your paper before you get to the final version. Three to four drafts are quite to be expected in writing a good
philosophy paper, especially if this is your first attempt. Show your drafts to me or to a tutor for comment
and suggestions.
3. THOU SHALT STATE THY ARGUMENT IN A VALID FORM: Choose a deductive method of reasoning
to compose your arguments. This could be a series of standard form categorical syllogisms where each
conclusion serves as the major premise for the succeeding argument until you arrive at the main argument
also stated in standard form categorical syllogistic form. Choose one of the 15 Valid Forms.
4. THOU SHALT PROVE YOUR ARGUMENT(S) VALID: Once your argument is formulated using one of
the known 15 valid standard form categorical syllogisms you must then prove validity of your argument.
You do this by use of a VENN DIAGRAM and The 6 Rules for Validity in Standard Form Categorical
Syllogisms. Embed the Venn Diagram for your thesis argument in the body of your text. Parse your
argument through each of the 6 Rules. DO NOT FAIL TO DO THIS! If you have mastered these techniques
you should have no trouble getting to this point. If you have trouble, see a tutor or bring your work to class
for analysis. I’ll be happy to evaluate it with you.
PART TWO OF YOUR TERM PAPER: SOUNDNESS
5. THOU SHALT ANALYZE THE SOUNDNESS OF THY ARGUMENT: Once your argument is proven
VALID then each of the premises for the main argument must be submitted to inductive analysis to
determine their empirical probability. Here you need to state the empirical conditions under which they
could be tested. Of course, if your argument contains terms and propositions about those terms that are
beyond the realm of empirical proof then you must state why that is the case. Then you must present an
'analytical' proof for your premises. THIS IS A CRUCIAL STEP IN YOUR PAPER. Valid arguments are easy
to construct since validity is purely a matter of correct form. Sound arguments, on the other hand, are valid
arguments that have all factually true, empirically verifiable, scientifically demonstrable premises to a high
degree of probability. If you find that the premises have scientifically weak evidence then you cannot claim
soundness for your argument, just weak probability. Empirically weak arguments provide little reason to
accept them as factually true. Don’t be shy to come to this conclusion if the evidence warrants it. That’s the
point of doing the paper, i.e. to see if valid and sound reasoning can substantiate the truth-claim of your
term paper thesis.
6. THOU SHALT SUMMARIZE THY FINDINGS: As a last step in your paper, review where you began,
where your inquiry took you and where you concluded. If this process changed your views on the issue
underlying your thesis then state the reasons why. If you discover that there is little or no empirical
verification for the factual truth of your premises, then say so. If you have come to some original insights
about this issue, then state what those insights are. Typically, your summary paragraph will be quite short.
7. THOU SHALT MAKE THY PAPERS printed 6-10 pages in length, double-spaced, spell-checked and
grammar-checked documents. Make two copies of your final paper. Keep a backup copy in digital format.
8. THOU SHALT FOLLOW APA (American Psychological Association) style and format for printing your
final paper. List all references and resources used according to the APA format.
9. THOU SHALT NOT COVET THY NEIGHBORS WORK. I define plagiarism as submitting the work of
another as if it were your own.
10. REMEMBER TO READ THY PAPER ALOUD: Before you hand in your paper READ IT ALOUD to
yourself and/or to a kind friend. You will catch last minute mistakes this way as well as enjoy a sense of
confidence that your final paper actually makes well-reasoned sense.
GRADING:
Your papers will be graded according to the following criteria:
1. Is it clearly written, relatively free from careless errors in typing, spelling grammar and syntax? I stop
reading papers that are syntactical train wrecks and do not grade them.
2. Is your thesis free from vague and ambiguous language?
3. Is there a logical flow to the structure of the paper?
4. Did you prove your argument valid by formal means?
5. Did you fairly represent the views of those you cite?
6. Did you consider counter arguments to your own?
7. Did you adequately examine the soundness of the premises you use?
8. Did you comprehend what you have been able to demonstrate?
9. Did you hand your paper in on time?
10. Did you do original work?
Excellent Internet resources for writing a philosophy paper:
APA Style and Format
Help with Writing
Here are some Valid Syllogisms from successful former student Term Papers. These thesis arguments were
successful, not because of 'what' they argued, but rather by 'how' they were argued.
AAA-1 BARBARA
All individual passion is ruled by individual character. All individual destiny is ruled by individual passion.
Therefore,All individual destiny is ruled by individual character.
EAE-1 CELARENT
No human fetus killing is a private matter. All human abortions are human fetus killings. Therefore, no
human abortion is a private matter.
(NOTE: by converting the MAJOR premise, this argument could be formulated as a CESARE, EAE-2)
AII-1 DARII
All perception states are real states. Some dream states are perception states. Therefore, some dreams
states are real states.
(NOTE: by converting the MINOR premise, this argument could be formulated as a DATISI, AII-3)
AII-3 DATISI
All things in life that don’t kill you are things that can make your character stronger. Some things in life that
don’t kill you are “bad choices” you make. Therefore some “bad choices” you make are things that can make
your character stronger.
(NOTE: by converting the MINOR premise, this argument could be formulated as a DARII, AII-1)
EIO-1 FERIO (All EIO Mood arguments are valid regardless of Figure)
No inanimate three-dimensional objects are objects that can commit murder. Some things (i.e. guns) are
inanimate three-dimensional objects. Therefore, some things (i.e. guns) are not objects that can commit
murder.
AEE-2 CAMESTRES
All state sanctioned marriages are marriages wherein it is at least logically possible for human procreation
to happen. No marriages between members of the same gender are marriages wherein it is at least logically
possible for procreation to happen. Therefore, no marriages between members of the same gender are state
sanctioned marriages.
EAE-2 CESARE
No ‘entity’ is a thing that exists outside of sense perception. All ‘god’ things are entities that exist outside of
sense perception. Therefore no ‘god’ thing is an ‘entity.’
(NOTE: by converting the MAJOR premise, this argument could be formulated as a CELERANT, EAE-1)
AOO-2 BAROKO
All 'gay' people are people that politicize their homosexuality. Some homosexual people are not people that
politicize their homosexuality. Therefore, some homosexual people are not 'gay' people.
OAO-3 BOKARDO
Some people that rely on ‘feelings’ in place of ‘reason’ are not ‘critical thinkers and writers’. All people that
rely on ‘feelings; in place of ‘reason’ are political ‘liberals.’ Some political ‘liberals’ are not ‘critical thinkers
and writers.’
EIO-2 FESTINO
No drugs are “recreational”. Some ‘high risk’ sports are “recreational.” Therefore, some “high risk” sports
are not drugs.
(NOTE: by converting either the MAJOR or MINOR premise this argument could be formulated as a
FERISON- EIO-3 or a FRESISON, EIO-4)
Many students have asked for a sample term paper that satisfies the necessary and sufficient conditions for
formulating a successful term paper in this course. Here is just such an example as your guide. Click the link to
access the PDF,
Sample Term Paper by Matthew Bixby class of 2007
Yet More resources on Writing a Philosophy Paper
Professor Douglas Portmore, Arizona State University has an excellent PDF that both parrallels these guidlines
and provides an excellent bibliogrphy for successful writing of undergraduate philosophy papers. Here's the
URL for his PDF
http://www.public.asu.edu/~dportmor/tips.pdf
---Cordially
Professor Mark McIntire
2
3
Copyright
© 2013
REASON ARGUE REFUTE:
Critical Thinking About Anything by Mark
McIntire
ISBN: 978-0-615-80070-7
ALL RIGHTS RESERVED: No part of this book may be
reproduced or transmitted in any form or by any means, electronic
or mechanical, including photocopies, recordings, internet,
multimedia, television, virtual reality, or by any information storage
and retrieval system, without permission in writing from Mark
McIntire.
MAY BE SOLD BY AUTHORIZED DISTRIBUTORS ONLY
First Printing 2007
Thank you for protecting the digital property rights
of the author.
4
Table of Contents
Copyright
Author: Mark McIntire
Dedication and Acknowledgments:
Part One: Reason
Section 1
Basic Logic Concepts
Section 2
Twenty Basic Reasoning Distinctions
Section 3
Reasoning Fallacies in Three Categories: Irrelevance, Presumption and Ambiguity
Section 4
Fallacies of Irrelevance Category
Section 5
Fallacies of Presumption Category
Section 6
Fallacies of Ambiguity Category
Section 7
Part One Reasoning: Learning Review
5
Section 8
Attributes of Critical Thinkers and Writers
Part Two: Argue
Section 2 Categorical Logic
Section 3
Categorical Propositions
Section 4
Categorical Syllogisms
Section 5
Venn Diagrams & 15 Valid Forms
Section 6
The Six Rules of Validity
Section 7
Problems with Ordinary Language
Section 8
Propositional Logic Overview
Section 9
Argument Learning Review
Part Three: Refutation
Section 1
Section 2
Refute the Definitions
Section 23
Refute the Logic
Section 4
Refute the Weak Evidence
Section 5
Refute by Analogy
Section 6
Refute Ethical Or Moral Assumptions
Section 7
Part Three:
Refutation Learning Review
Appendix I: Guidelines for Argumentative Writing
Appendix II:
Writing a Journal of Your Ideas
Bibliography
Bibliography
Appendix III
The 19 Rules of Natural Inference
6
7
Author: Mark McIntire
Born in Salem, Massachusetts, Professor McIntire received his
undergraduate and graduate philosophy degrees from Oblate College at
The Catholic University of America in Washington, D.C. In 1977 he wrote
an original one-man-show, “JFK: A Time Remembered” giving over 500
live performances at colleges and universities across America.
Author of “The Financial Core Handbook”, Professor Mark McIntire has
taught Philosophy since 1966 at Westfield State College, Massachusetts
(now Westfield State University), University of Phoenix, Antioch University,
and currently teaches online at Santa Barbara City College in California.
McIntire was elected to the National Screen Actors Guild Board of Directors
in 1983, when he wrote and filed a brief, amicus curiae, with the Supreme
Court of the United States in the landmark case CWA v Beck (1986). The high
court decision 5-3 sustained McIntire’s argument protecting the freedom of dissident
union workers and led to the publication of his work “The Financial Core
Handbook” that remains the definitive source on this decision to date.
When not teaching Critical Thinking and Writing at Santa Barbara City
College online, McIntire conducts executive seminars in “Critical
Thinking for Success” and mentors gifted students into their graduate
degree programs.
In 2010, “The Mark McIntire Show: “MINDS THAT MATTER” ran for 52
episodes on AM 1290 Santa Barbara News Press Radio. The highly rated
program featured the life of ideas from college presidents, writers, actors,
and scientists and gifted students
Supplemental materials for this e-textbook, Reason Argue Refute:
Critical Thinking About Anything, are available on Mark McIntire’s
online teaching website:
http://markmcintire.com
8
9
Dedication and Acknowledgments:
It seems fitting for an author of an Aristotelian
categorical logic book to acknowledge his
indebtedness to others by logical category.
In Memoriam: Dr. Peter A. Angeles, Joan
McIntire, Ron Pagel, Vernon Olson,
Richard Roberts
Inspiration: Many thousands of students I have
taught since 1966
Nurturing: David L. Hutchinson, Ellen White,
Tyler and Whitney Duncan
Guidance: Charlton and Lydia Heston, Fraser C.
Heston, Christopher Mitchum, Carol Lanning
Wisdom: Matthew Kane Bixby, Professor Joseph
White, Professor Jim Chesher, Professor Peter
Georgakis, Preparation: Mychilo S. Cline,
Patricia L. Raabe, Norman P. Stevens, Max
Holihan
Insistence: Christopher Candy, Gary Gentilini,
Michael Miller, Mikal C. Davies, Alastair
Patterson
Patiently, you have coaxed this book from me.
-Cordially, Mark McIntire “Nemo dat...quod non
habat."
10
Preface and Introduction
“Is not the great defect of our education
today--a defect traceable through all the disquieting symptoms of trouble
that I have mentioned-that although we often succeed in teaching our
pupils "subjects," we fail lamentably on the whole in teaching them how
to think: they learn everything, except the art of learning.”
---‘The Lost Tools of Learning’ by Dorothy Sayers, Oxford University,
1947
Welcome to a critical thinking boot-camp for the mind. This is a “how to
think” e-textbook for digital devices. Any intelligent person over the age of
twelve years old can master basic reasoning, argumentation, and refutation
by using this book. Primarily intended for high school college and
university students, it can also serve the needs of career professionals in their
writing and decision making. Tim McGrath, author of, John Barry: An
American Hero in the Age of Sail wrote a gracious testimonial after using
this book; “In no small thanks to Reason, Argue, Refute, I wangled a nice
advance for a book on the Continental Navy (the Reason section was
obviously a bigger help in this instance than the other two – but man, have
they been good to learn for the business hours of the day).”
This book presents the basics on ‘how to think’ clearly, rationally and
logically. The guiding compass of the entire text is the concern for the quality
of “how” students think, not with the quantity or content of ‘what’ they
think. It is divided into three main parts, each with relevant subsections.
Part One: Reasoning gives rigorous training in basic logical ideas, laws,
methods and principles as well as an exposition of common fallacies in
everyday failed attempts at reasoning.
Part Two: Argument gives systematic training in recognizing
arguments by type distinguishing arguments by the strength of the inference
in their conclusions, analyzing arguments in ordinary language and
everyday speech, formulating arguments using both categorical and
propositional logic, proving the validity of arguments by formal rules and
graphic illustration, and distinguishing between valid and sound
arguments.
Part Three: Refutation gives effective strategies for refuting arguments
by objecting to definitions, weak inductive evidence, causal claims,
analogies, and ethical and moral first principles. Ways to look inside (X11
ray or autopsy) arguments for their internal defects are demonstrated
leading to cogent refutation by formulating contrary, contradictory and
analogical counter arguments.
Appendix I offers argumentative writing guidelines that have proven
successful for thousands of students.
Appendix II offers a reliable format for anyone wishing to write and
keep a journal of their “life of ideas.”
Throughout this book provocative examples are used sparingly and only to
illustrate ideas and methods of effective reasoning, argument, and
refutation. This book helps fill a vacuum created by current education
curricula. Those curricula advocate teaching “what” to think while giving
only flimsy clues as on “how” to think. Current higher education
expectations place a premium on “diversity” of opinions while requiring
little if any formal training in how to determine valid and sound arguments
for or against these diverse opinions.
Why Read This Book? Now, at the beginning of the twenty-first century
it is common for students to receive a Bachelor’s, Master’s, and even a
Doctoral degree from higher education institutions without ever being
formally trained in reasoning, argumentation, and refutation. This fact
adequately explains the disappointing failure of higher education
globally to reliably educate individuals who know “how” to think. The
growing demand for “Critical Thinking for Success” training seminars
for business managers gives even more evidence of the neglect of critical
thinking in schools, colleges and universities. Even worse, in many
instances what passes as training in critical thinking, even at university
level, is little more than asking students, “Well...how do you feel about
that?”
Why do students need to learn “how” to think formally? To answer
this question we need to recall that higher education policy in the late
1960’s shredded the “core curriculum” for a variety of well intentioned
but ultimately calamitous reasons. Prior to the early 1970s no college
student could earn a degree in the arts and sciences without required
formal training in the processes of reasoning and argumentation in the
core-curriculum. This formal training was usually, but not exclusively,
conducted by the philosophy department faculties. Some Math courses
and some English courses also fulfilled this requirement, and still do to
12
this day. The point is that, prior to the early 1970s, the requirement for
formal training in formal reasoning was fundamental to the very notion
of a liberal arts education of receiving a Liberal Arts education.
All that changed as “cultural relativism” and “social diversity”
gradually became the expected outcomes in much of the American
higher education curricula into the mid 1970’s and beyond. By the time
the graduates of this “outcome based” curricula became teaching faculty
themselves through the 80’s, 90’s, and on into the new millennium, little
trace of a common logic could be found throughout many academic
curricula. Standards for testable proof also eroded with the rising tide of
“cultural relativism.” In some curricula, the systematic denial of reason
based on logic and best evidence became common while the academic
disciplines fragmented. Settling academic debates became more a matter of
advocating a preconceived notion of ‘social justice’ rather than
conducting critical thought. Everyone’s opinion was (and in some cases
still is today) viewed as equally valid and sound regardless of its logical
absurdity or lack of testable evidence. While this erosion of academic
standards progressed, many astute intellects objected strenuously to a
lowering of academic reasoning standards. The citation above by Dorothy
Sayers is only one example and that was delivered over forty-five years
ago.
“From the twelfth century through the early twentieth century,” wrote
Margaret Ferguson of Yale University in 1977, “the curriculum of the
western university put great emphasis on the arts of argumentation—the
arts of Aristotle called dialectic and rhetoric and distinguished from all
other branches of human knowledge on the basis of their capacity to
draw opposite conclusions impartially. Teachers and students, people at
every level of the university’s hierarchy, were continually practicing and
developing argumentative skills…the university provided a forum in
which critical thinking (within certain limits) was not only allowed but
encouraged…The problem we face today…is that the enabling conditions
of debate are atrophying both within the university and in its relations to
society…What I propose is that the university should spend time and
some of its dwindling money on devising ways to preserve genuine
debate” [Yale Magazine and Journal, November 1977, p.11.] Her
admonition was swept aside while academic curricula were reshaped
according to the new canons of ‘social justice’ and ‘social outcomes’. The
underlying assumption of this book is the notion that rational thinking is
13
a cultivated art that applies the discipline of logic and search for best
available evidence to any debatable topic in any academic discipline.
Neither of these alone is sufficient for cultivating the art of critical
thinking. Both are, however, necessary conditions for the life long process
of a rational thinker seeking truth and wisdom.
Reasoning beyond our feelings is the sub textual premise for this book.
However, it would be a gross miscalculation to infer from this that the
author underestimates the role of our emotions in the seeking of happiness
in wisdom. On the contrary, no rational person could exit the bed in the
morning without the stir of passion to think, act, and change the world
into a better place. Finding truth through reason, however, entails a
marriage of emotion tempered by intellect. Otherwise we would do better
to stay in our beds.
Why is this book superior to other books already available? Unlike
most critical thinking books now flooding the market, this text does not seek to
entertain, or to incite with ideological bias. Rather, it provides grounding in
the basics of artful reasoning that has stood the test of time and application.
This book is a bare bones, no nonsense instruction in how to seek truth
through logic and best evidence. Reason Argue Refute: Critical Thinking
About Anything includes a unique feature not found in any other book
currently available to serious students of reasoning and argumentation.
Almost one-third is devoted to mastering the ultimate power of any well
trained mind, the power of refutation. This book provides sound
strategies not only for refuting the arguments of others, but more
significantly, for testing the arguments we formulate ourselves. Reason
Argue Refute: Critical Thinking About Anything was suggested by
Professor Gary Gentilini of the University of Phoenix. Thank you, Gary.
Introduction.
Contrary to what some educators may claim, there are ‘good’ arguments
and there are ‘bad’ arguments and we can tell the difference. When we
use logic backed by best evidence we make good arguments. If our logic
is defective and/or if our evidence is weak, then we make bad
arguments. Critical thinking entails knowing the difference between the
two, and then applying good arguments and refutations to debatable
topics among reasonable people.
This book will teach you how to think, not what to think. The good
news is that we are all born with the ability to think. Unfortunately, only a
14
few of us are ever trained how to think clearly, precisely, and consistently
regardless of the subject matter on a consistent basis. That’s what this book will
do for you; give your thinking a reliable structure to ensure good
reasoning for the rest of your life of ideas. This will be done by sorting
out failed attempts at reasoning called informal fallacies from successful
acts of reasoning called sound argumentation. We use logic to sort things
out. We use best available evidence to separate good, better, and best
arguments from weak, defective and worst arguments. This book will
teach or improve your ability to use both in serious debate and discourse.
If you want to apply good reasoning to your written es says and term
papers, then study Appendix I. Have you ever wanted to keep a personal
journal of your ideas? If so, then implement the format for writing your
journal of ideas in Appendix II. We begin our study of critical thinking and
writing by understanding the process of reasoning.
Here, we begin our mastery of the critical thinking and writing arts and
methods by stipulating: Twenty Distinctions for Critical Thinkers. If you get
nothing more from this book other than these reliable mental distinctions they
will bring clarity to your perception, coherence to your ideas and effective
tools to dissect ideas and arguments from opinions. They form the conceptual
core of this work. Here they are. Later, they will be presented again with
examples:
Twenty Distinctions for Critical Thinking
Beliefs / Knowledge: Beliefs are opinions we accept as true or
•
false. Knowledge is accepting beliefs when confirmed by logic and best
evidence.
Sentence / Proposition: Any syntactically and grammatically
•
correct group of words is a sentence, whereas only those sentences that
state a claim is either true or false are propositions.
Syntax / Grammar: The general rules for ordering words in a
•
language is syntax, whereas the specific set of rules for proper usage of
words in a language is grammar.
Assumption / Presumption: Any claim accepted as true in
•
reasoning to another claim is an assumption, whereas a presumption is
using an assumption in the process of reasoning.
Connotation/Denotation: In logic, the unique qualities or
•
attributes common to all referred to by a term is its connotation, whereas a list
15
of only those individual things having those unique qualities or attributes
constitutes a term’s denotation. (Note: Other academic disciplines ascribe
broader associative meaning to “connotation.”)
Subjectiveclaim/Objective claim:Any truth claim that cannot be
•
independently verified as true or false is a subjective claim, whereas any
truth claim that can be independently verified as true or false is an objective
claim.
Imply / Infer: To leave conclusions that may be drawn by
•
others is to imply. To draw conclusions from what is implied is to
infer.
Explanation / Argument: Explanations provide information
•
about who, what, how, when, where, and even why a statement is either
true or false; whereas arguments provide reasons for accepting that the
statement is either true or false.
Premise / Conclusion: A premise is a
•
Proposition offered as a reason for accepting the truth or falsity of
another proposition called a conclusion.
Formal / Informal Argument: A formal argument is any argument that
has all stated premises a n d a stated conclusion according to an
established pattern of inference. An informal argument may have
missing premises that are thought to be reasonable assumptions in a
pattern of reasoning.
Logic / Rhetoric: Logic is the study of making inferences in the
•
process of reasoning. By contrast, Rhetoric is the art of evoking desired
responses by any linguistic means available.
Logical possibility / Empirical Probability: Any claim that does
•
not contradict itself is a logically possible claim. However, only logically
possible claims that can, in fact, be verified by observable, test able
evidence, are empirically probable claims.
Fallacy / Error: Fallacies, whether formal or informal, are
•
conclusions arrived at by some mistake in the process or pattern of
reasoning itself. Errors are merely cognitive miscalculations or
misperceptions.
Valid / Sound: A deductive argument is valid if the conclusion
•
follows from the premises by necessity, i.e., on the assumption that the
premises are true, then the conclusion would also have to be true. A
deductive argument is sound if, and only if a) it is valid, and b) the premises
of the argument are true according to best available evidence either
16
analytically or empirically.
Deductive / Inductive: When it is claimed that a necessary
•
conclusion is drawn out of premises given as reasons to accept it, then
that phase of the reasoning process is called deductive. When a “probable”
or “likely” conclusion is projected from verification of instances cited,
then that phase of the reasoning process is called inductive. Inductive
probability can range anywhere from “weak” to “strong.
Necessary Conditions / Sufficient Conditions: Any elements
•
required for events to take place are known as necessary conditions. Any
elements that are enough for something to take place are known as the
sufficient conditions.
Causes/Effects: Those necessary and sufficient conditions
•
thought to be required in order for another event to take place are called
causes. Any events that result from those necessary and sufficient
conditions actually taking place are called effects.
Analytic / Synthetic: Propositions derived from a purely mental
•
examination of ideas and their elements are analytic. Propositions
determined as true or false from observations or facts are synthetic.
a priori / a posteriori: Knowledge independent of observation is a
•
priori knowledge (Latin: a priori, before the fact). Knowledge after
observation is a posteriori knowledge (Latin: a posteriori, after the fact).
Ethical Principles / Moral Codes: Any set of general rules or
•
laws thought to govern human conduct constitutes ethical principles. Any
set of maxims, guides, or precepts that apply ethical principles to
particular human conduct constitutes moral codes.
17
Part One: Reason
18
Section 1
Basic Logic Concepts
Working Definitions of Basic Logic Concepts:
Truth: Any claim to fact that is analytically or empirically verified to
coherently and consistently correspond to both the rules of precise
definitions, and formal logic backed by best available evidence; that cannot
be falsified.
Proposition: Any sentence that claims something is true or false either
analytically or empirically.
Argument: Any set of propositions (premises) that provide reasons to
infer the truth or falsity of another proposition (a conclusion) either
deductively or inductively.
Inference: Any mental process that draws a conclusion truth
claim from premise truth claims.
Premise: Any proposition that is used as a reason to infer the
acceptance of another proposition
Conclusion: Any proposition that is inferred from a set of premises.
Deduction: Any inference processes that ‘draws out’ one proposition
(conclusion) from other propositions (premise or premises) by necessity.
(Latin: deduco, to lead out of or from)
Induction: Any inference processes ‘leading up to or away from’, a
probable conclusion that seems likely based on sufficient individual
instances being enumerated. (Latin: induco, to lead up to.)
Explanation: Any set of statements that answer the, who, what, when,
where, how, or even why questions of any physical or mental event.
Valid Argument: Any deductive reasoning process that entails a
conclusion from stated premises by logical necessity such that if the
premises are true then the inferred conclusion must be true as well.
Invalid Argument: Any deductive reasoning process that fails to entail its
conclusion from its states premises by logical necessity.
Soundness: When any valid deductive argument is composed of all
19
analytically or factually true premises.
Cogency: Any line of reasoning that is clear, logical sound and
convincingly backed by testable evidence.
Rhetoric: Any use of language or image purely calculated to persuade
regardless of factual truth or logical validity.
Logic: Formal study of ideas, laws, rules, or methods that ensure
conclusions follow from premises either by deductive necessity called
‘entailment’, or by inductive probability.
Categorical Logic: First codified by Aristotle (and hence sometimes
called Aristotelian logic), refers to the rules for necessary inferences about
members of one class being included as members, or excluded as members
of another class, set, group or category. Propositional Logic: A system of
symbols (and hence sometimes called symbolic logic) standing for whole
or partial propositions, related by logical operators (‘and’, ‘or’,
‘if...then’ etc.) that connect whole or partial propositions resulting in
necessary inferences construed as the ‘Rules of Natural Inference’.
Note: These are working definitions only. They are not offered as final,
precise definitions that resolve all legitimate philosophical debate. Other
academic disciplines have different, more specific definitions that are
proper for their field of study. Beginning students of critical thinking and
writing can use these definitions to stimulate larger philosophical debate
as they move through this text.
20
Section 2
Twenty Basic Reasoning Distinctions
Good distinctions are the sharp knives of reasoning. To better understand
our basic definitions used in the process of reasoning, it is essential to
make a list of useful, basic linguistic distinctions. When we make good
distinctions between ideas we understand how they differ from each
other. If we understand how two ideas differ from each other, then we
understand more clearly what those ideas really mean. Conversely, when
we fail to make necessary distinctions in the meaning of ideas we run the risk
of falsely supposing that there is little or no difference between ideas that
are, upon reflection, quite different. Good reasoning requires that words
have definite and discernible meanings through distinctions.
The following list of basic distinctions, once mastered, provides students
with invaluable ‘cutting tools’ that reveal what ideas really mean, and,
sometimes more significantly, what ideas do not mean. As you read them,
think of them as a dialogue of differences. Try to formulate examples that
illustrate these distinctions in your notebook. Use these distinctions to keep a
journal of your ‘life of ideas’. If you learn nothing more than these twenty
distinctions, your investment in this book will pay dividends in better
reasoning skills for life.
Students who master these distinctions report greater ‘clarity’ and
‘precision’ in reasoning. Whereas they formerly used these terms
interchangeably, now they choose their words more carefully with
gratifying results in the quality of their reasoning. Good reasoning begins
with precisely distinguishing differences between ideas in any debate.
Here, then, is the list of twenty essential distinctions for critical thinking
in the reasoning process.
Beliefs / Knowledge: Beliefs are opinions we accept as true or false.
Knowledge is accepting beliefs when confirmed by logic and best
evidence.
Examples: “In my opinion, all swans are white.”
(Belief). “With the discovery of black swans in Australia, I now know that
not all swans are white. Some swans are black.” (Knowledge)
Sentence / Proposition: Any syntactically and grammatically correct group
21
of words is a sentence, whereas only those sentences that propose that a
given claim is either true of false are propositions.
Example: “Close that door!” is a proper sentence, but it is not a
proposition. “All Popes are Catholics.” is a proposition (truth claim) as
well as a proper sentence. Not all sentences are propositions, but all
propositions are sentences.
Syntax / Grammar: The general rules for ordering words in a language is
syntax, whereas the specific set of rules for proper usage of words in a
language is grammar.
Example: “Up with put, I will not you.” This sentence violates the rules of
syntax in the English language.
“There’s keys on the table.” is a sentence that violates the rules of
grammar in the English language.
Assumption / Presumption:Any claim accepted as true in reasoning to
another claim is an assumption, whereas a presumption is using an
assumption in reasoning.
Example: “Based on the assumption that you want to earn your own keep
around here, I presume you are looking for gainful employment.”
Connotation / Denotation: In logic, the unique qualities or attributes
common to all referred to by a term is its connotation, whereas a list of
only those individual things having those unique qualities or at tributes
constitutes a term’s denotation. (Note: Other linguistic studies ascribe
broader associative meaning to connotation.)
Example: Article 1, Section 3 of the United States Constitution enumerates
the exclusive attributes and requirements necessary for the connotation of
the term ‘United States Senator’. A complete list of all those who ever did
have, or do now have these exclusive at tributes, and fulfilled these
requirements is the denotation of the term ‘United States Senator’.
Subjective claim/Objective claim: Any truth claim that cannot be
independently verified as true or false is a subjective claim, whereas any
22
truth claim that can be independently verified as true or false is an
objective claim.
23
Example: “My daily horoscope is true for me.”(Subjective claim) “A fire
will not occur without fuel, oxygen, and a source of combustion.”
(Objective claim)
Imply / Infer: To leave conclusions that may be drawn by others is to
imply. To draw conclusions from what is implied is to infer.
Example: “She inferred what you implied.”
Explanation / Argument: Explanations provide information about who,
what, how, when, where, and even why a statement is either true or false;
whereas arguments provide reasons for accepting that the statement is
either true or false.
Example: Planets are celestial bodies in a solar system that dominate
their orbit around a central sun. (Explanation about what a ‘planet’ is.)
Celestial bodies whose orbit is not disturbed by other celestial bodies are
‘planets’. Pluto’s orbit is disturbed by other planets. Therefore, Pluto is not
a ‘planet’. (Argument against Pluto being a planet)
Premise / Conclusion: A premise is a proposition offered as a reason for
accepting the truth or falsity of another proposition called a conclusion.
Example: “If I want to stay healthy, then I should stop smoking cigarettes
(premise). I want to stay healthy (premise). Therefore, I should stop smoking
cigarettes (conclusion).
Formal / Informal Argument: A formal argument is any argument that
has all stated premises and a stated conclusion according to an established
pattern of inference. An informal argument may have missing premises
that are thought to be reasonable assumptions in a pattern of reasoning.
Example: “Monkeys climb trees. I am a monkey. Therefore, I climb
trees.” (Formal argument) “No, I don’t climb trees; I’m no monkey.”
(Informal argument)
24
Logic / Rhetoric: Logic is the study of making inferences in the process of
reasoning. By contrast, Rhetoric, in its primary meaning, is the art of
evoking desired responses by language, speech or image.
Example: If you bought this book because you thought that the
contents might help you in your study of critical thinking, then you inferred
reasonably by logic. If you bought this book solely because your mother told
you to, then you were persuaded by bad rhetoric.
Logical possibility / Empirical Probability: Any claim that does not
contradict itself is a logically possible claim. However, only logically
possible claims that can, in fact, be verified by observable, testable
evidence, are empirically probable claims.
Example: Given certain assumptions, ‘time-travel’ is certainly logically
possible, but it is not yet empirically probable.
Fallacy / Error: Fallacies, whether formal or informal, are conclusions
arrived at by some mistake in the process or pattern of reasoning itself.
Errors are merely cognitive miscalculations or misperceptions.
Example: “No one’s ever disproved astrology, so therefore the claims
of astrologists must be
True”. (Fallacy from ignorance) “Anyone born in April is a ‘Leo’.
(Astrology error)
Valid / Sound: A deductive argument is valid if the conclusion follows
from the premises by necessity, i.e., on the assumption that the premises
are true, then the conclusion would also have to be true. A deductive
argument is sound if, and only if a) it is valid, and b) the premises of the
argument are true according to best available evidence either
analytically or empirically.
Example:All light bulbs are human.
All Bostonians are light bulbs.
Therefore, all Bostonians are human.
(Valid but not sound.)
No light bulbs are human. All Bostonians are human.
25
Therefore, no Bostonians are light bulbs.
(Valid and sound)
Deductive / Inductive: When it is claimed that a necessary conclusion is
drawn out of premises given as reasons to accept it, then that phase of the
reasoning process is called deductive. When a ‘probable’ or ‘likely’
conclusion is projected from confirmation of instances cited, then that
phase of the reasoning process is called inductive. Inductive probability
can range anywhere from ‘weak’ to ‘strong’, but never absolutely certain.
Examples: “All classes currently taught at City
Colleges are taught by highly qualified professors. Critical Thinking and
Writing is a course currently taught at City College; therefore, Critical
Thinking and Writing currently taught at City College is taught by highly
qualified professors.” (Deductive argument)
“My brother took classes at City College last semester and all were taught
by highly qualified professors. My sister took classes at City College last
semester and she reports the same thing. In all probability, the classes I take
at City College next year will be taught by highly qualified professors as
well.”
(Inductive argument)
Necessary Conditions / Sufficient Conditions: Any elements required
for events to take place are known as necessary conditions. Any elements
that are enough for something to take place are known as the sufficient
conditions.
Example: The precise moment of ignition, by any means, is the
sufficient condition for the necessary conditions of fuel, oxygen, and
source of ignition to actually take place in a fire.
Causes/Effects: Those necessary and sufficient conditions thought to
be required in order for another event to take place are called causes. Any
events that result from those necessary and sufficient conditions actually
taking place are called effects.
Example: Sparks from a welder’s torch on the roof of the building
26
showered down on a stack of gasoline soaked newspapers several floors
below (causes). As a result the building caught fire and was destroyed
(Effects).
Analytic / Synthetic: Propositions derived from a purely mental
examination of ideas and their elements are analytic. Propositions
determined as true or false from observations or facts are synthetic.
27
Example: (analytic proposition) “If
he’s a bachelor, then he’s not
married.” (Synthetic proposition)
“The City of Chico, California is
approximately 476.4 miles from the
city of Santa Barbara.”
a priori / a posteriori: Knowledge
independent of observation is a
priori knowledge (Latin: a priori,
before the fact). Knowledge after
observation is a posteriori
knowledge (Latin: a posteriori, after
the fact).
Example: (a priori) “Squares are
four sided figures.” (a posteriori)
“This square is half the size of that
square.”
Ethical Principles / Moral Codes:
Any set of
General rules or laws thought to
govern human conduct constitute
ethical principles. Any set of
maxims, guides, or precepts that apply
ethical principles to particular human
conduct constitutes moral codes.
Example: (ethical principle)
“Treating others as we would wish to
be treated is our duty as human
beings.” (Moral code) “Do no
harm.” (Hippocratic Code)
28
29
Section 3
Reasoning Fallacies in Three Categories: Irrelevance, Presumption
and Ambiguity
Fallacies are failed attempts at reasoning. Part of knowing what
successful reasoning is entails knowing what successful reasoning is not.
We now take up the study of informal fallacies in the process of reasoning.
Reasoning fallacies are not like errors of fact, they are mistakes in the
process of thinking. Like some lost traveler, fallacies happen when the
mind takes a wrong turn trying to negotiate an inference. You can make an
error in trying to balance your checkbook, but it would be improper to
accuse you of committing an informal fallacy. However, you can be
accused of committing an informal fallacy if, in the act of reasoning, you
are vague, ambiguous, careless, presumptive, or allow some unrelated
factors to mistakenly divert your premises from a necessary conclusion.
These reasoning mistakes are quite common in every day discourse. We
need not strain hard to find news reports, film ‘documentaries,’ TV
commercials, internet ‘blogs’, serious discussions, and debates in public
and private life replete with informal fallacies of reasoning. We are all
human and we all commit these mistakes in reasoning though we are
slow to admit it, and quick to point it out in others. Critical thinkers
and writers, however, constantly develop the necessary self-discipline to
both recognize and eliminate these mistakes in their reasoning process.
Note that informal fallacies are often mixed, by clever minds, into
‘cocktails’ of several fallacies all in the same argument. Often it’s a
powerful brew concocted by those with full intent to deceive their
audience. It is also noteworthy that these informal fallacies are sometimes
not only deliberately committed in order to deceive those seeking truth,
but also to intentionally coerce some action on the part of the listener or
reader. Manipulation of public and private opinion is serious big business
in the age of media technology. Worse still, deliberate distortion of fact
through informal fallacies is a nonpartisan, nonsectarian, equal opportunity,
intellectual sport for some. Today’s political ‘Gotcha-Culture’, the new
shortcut to fame, money and power, is as invidious as it is insidious.
Critical thinkers need to beware.
Example: “If you’re not a progressive thinker, then you must be
stupid.’”(You could substitute any political ‘stereotype’ with the same
30
resulting fallacy.)
As you read this section on informal fallacies you will find some of them
humorous. You will ask yourself, “How can anyone think that way?” Look
in the mirror. For easy study purposes and logical arrangement, we divide
these reasoning mistakes into three categories, and then we subdivide
these into members of those categories. Examples are given but you will
do yourself a great service if you keep a record of the informal fallacies you
encounter in your daily routine. Put them in your journal of ideas. Read them
to your children. They will thank you.
There are three main categories of informal fallacies:
Informal Fallacies of Relevance:
In fallacies of relevance, arguments rely on premises which may seem
related to the conclusion, but which in fact are not. Relevance here is
understood as being related to the issue under debate.
Informal Fallacies of Presumption:
Fallacies of presumption contain dubious or false premises in need of
factual proof that are simply assumed to be true. Presumption here is
understood as being an unquestioned acceptance.
Informal Fallacies of Ambiguity:
In fallacies of ambiguity, reasoning goes awry because words, phrases, or
entire propositions with more than one clear, definite meaning in the
argument are misleading and therefore cannot imply the conclusion with
logical necessity. Ambiguity here is understood as being confused about
exact meaning. Many of these informal fallacies have Latin names that
have passed into common usage. Therefore, our discussion includes their
Latin etymology in parenthesis; to better enlighten serious students of
reasoning. Now we master the most common informal fallacies in each
category. First, let’s consider major examples of relevance fallacies
31
Section 4
Fallacies of Irrelevance Category
Irrelevancies derail reasoning. Fallacies of Relevance rely on premises that
might seem to be related to the conclusion when, in fact, they are not related
necessarily or even accidentally. There are seven major fallacies of
relevance that we study here.
1. Argument from Ignorance(Latin:ad ignorantiam, from ignorance,):
When it is argued that a proposition is true because it has not been proved
false, or when it is argued that a proposition is false because it has not been
proved true then the ad ignorantiam fallacy is committed.
Example: Since no one has disproved the theory of evolution, the theory of
evolution must be true.
2. Appeal to Inappropriate Authority (Latin: ad verecundiam, from
respect,): When the premises of an argument appeal to the judgment of
some party or parties having no legitimate claim to authority in the
matter at hand, then the ad verecundiam fallacy is committed.
Example: Gloria Diva just returned from Berlin and she says that
Germany’s new chancellor, Adolph Hitler, is a compassionate leader of the
German people. That’s good enough for me because I love all Gloria’s
movies. If Gloria likes Herr Hitler, then he must be a kind leader of the
German people.
3. Argument Against the Person(Latin: ad hominem, to the man or
person): When an attack is leveled not at the claims being made, or the at
the merits of the argument made, but directly at the person making the
argument, then it is a fallacy ad hominem. Arguments ad hominem come in
two flavors:
When the attack is directed against the person making a claim, seeking to
defame or discredit them as a person it is called an ‘abusive ad
hominem.’
Example: “Don’t believe anything he says. He never takes a shower.”
32
When the attack is indirectly against a person, suggesting that they hold
their views chiefly because of their special circumstances, interests or
associations, then it is a ‘circumstantial ad hominem’.
Example: “I find it interesting that all the Senators who voted for drafting 18
year olds into the military are themselves well beyond draft age.”
4. Appeal to Emotion(Latin:ad populum, to the populace): When
careful reasoning is replaced with devices calculated to elicit popular
enthusiasm and emotional support for the conclusion advanced, then
the ad populum fallacy is committed.
Example: So, our President lied about having extramarital sex in the Oval
Office of the White House. Cool! Everybody lies about sex.
5. Appeal to Pity(Latin:admisericordiam, from pity): When careful
reasoning is replaced by devices calculated to elicit pity from the listener
and to distract from the issue in question, then the ad misericordiam fallacy
is committed.
Example: “You can’t fail me in this course! I NEED this course to transfer to
University, and my parents will kill me if I don’t transfer this semester”.
6. Appeal to Force (Latin: ad baculum, to the stick): When careful
reasoning is replaced with direct or insinuated threats of force or
coercion to bring about the acceptance of some conclusion, then the ad
baculum fallacy is committed.
Example: “If you want that raise next month, you better endorse my uncle in
the next city council election.”
7. Irrelevant Conclusion (Latin: ignoratio elenchi, ignorance of
refutation) When the premises miss the point, purporting to support
one conclusion while in fact supporting or establishing another, then
33
the ignoratio elenchi fallacy is committed.
Example: “This is ridiculous. Here I am being ticketed and fined for
speeding while thugs roam the streets committing violent crimes at will.
The police should leave me alone and hunt down those dangerous
criminals.” It may be the case that the police need to hunt down violent
criminals. However, that is unrelated to deserving a ticket.
34
Section 5
Fallacies of Presumption Category
Buried assumptions are land mines in reasoning. The presumption
category of mistaken (fallacious) arguments arises from reliance on
propositions that are assumed to be true, but are in fact false, dubious or
without warrant by sufficient evidence. Here we explain the types of
reasoning mistakes in five fallacies of presumption:
1. Complex Question: When a question is asked in such a way as to
presuppose the truth of some assumption or question buried in the original
question, then the Complex Question fallacy is committed. The answer to
one question cannot be presumed in order to give evidence for another
question. The questions need to be ‘divided’ and each considered on its
own merits.
Example: “What color paint are you drinking today that makes you say
something that absurd?”
2. False Cause (Latin: post hoc, ergo propter hoc, after this, therefore
because of this): When one mistakes as a ‘cause’ some factor that is really
only a temporal sequence, correlation or association, then the False Cause
fallacy is committed. (Causal arguments are often difficult to prove
conclusively, as will be seen in Part Three: Refutation.)
Example: “My dad, cheated on his taxes last year, and his business went
belly-up this year. That’s how Karma works dude.”
3. Begging-the-Question: (Latin: petitio principii, seeing the premise):
When one assumes in the premises of an argument the very truth of what
one seeks to establish in the conclusion of that argument, then the petitio
principii fallacy is committed.
Example: “The reason I’m so popular is that everybody likes me.”
(Reputed quote from Muhammad Ali).
4. Accident: When one applies a generalization of a principle or general
rule to an unusual individual case that it does not properly govern, then
the fallacy of Accident is committed.
Example: Anyone swimming in the city reservoir will be prosecuted and
fined. The police should therefore arrest and prosecute the paramedic that
35
rescued a drowning child who fell into the reservoir.
5. Converse Accident: This is just
the reverse of Accident. When one
moves carelessly or too quickly from
an unusual single case to an
indefensibly broad generalization,
rule or principle, then the fallacy of
Converse Accident is committed.
Example: Oprah Winfrey is a
woman, and she is paid more money
than any male talk-show host.
Therefore, female talk-show hosts, as
a rule, are paid more money than
male talk-show hosts.
36
Section 6
Fallacies of Ambiguity Category
Mental misdirection is the basis of humor. When the mind is misdirected
by ambiguous words, phrases, signs, accents, even entire sentences there’s
usually a punch line soon to follow. When ambiguity infects reasoning
then erroneous conclusions usually result. Nothing can be inferred with
certainty from ambiguity because ambiguity means confusion of at least
two meanings. In these mistaken, but often funny, arguments reliance is on
some shift in the meaning of words, phrases, or even entire sentences, from
their meaning in the premises to some other meaning in the conclusion.
Professional comedians are keen practitioners of ambiguity fallacies. The
essence of humor relies on misperception. It is precisely this
misperception that enables ambiguity to lead us in mental misdirection
often with humorous but sometimes foolish mistakes in reasoning,
1. Equivocation: When the same word or phrase is used with two or
more meanings, deliberately or accidentally, in the formulation of an
argument, then the fallacy of Equivocation is committed.
Example: Rare books are expensive. Great novels are rare books.
Therefore, great novels are expensive.
2. Amphiboly: When one of the statements in an argument has more
than one plausible meaning, due to the loose or awkward way in which
the words in that statement have been combined, then the fallacy of
Amphiboly is committed.
Example: "Customers are required to remove all their clothes when dryer
stops.” (Amphibious sign in a Laundromat).
3. Accent: When a shift of meaning arises within an argument as a
consequence of changes in the vocal stress or graphic emphasis given to its
words, then the fallacy of Accent is committed.
Example:“My name is Schvink, and whadi-ya-think, I’ll press your
pants for nothing.” (When read with vocal accent of a declarative sentence, it
37
means that you get free pressing of your pants. However, when read with
the vocal accent of a question, it means; do you really think I’ll press your
pants for free? Are you
insane?
4.
Composition: This fallacy is committed: a) when one reasons
mistakenly from the attributes of a part to the attributes of the whole, or
b) when one reasons mistakenly from the attributes of an individual
member of some collection to the attributes of the totality of that
collection. The fallacy of Composition, and its sister fallacy of Division
are often referred to as ‘Part-To-Whole’ fallacies. Here’s why.
Example: I’m thinking of buying a new Macintosh e-book computer
and I found out that the onboard speakers are really inexpensive.
Therefore the laptop itself must be really inexpensive.
5. Division: Conversely, the fallacy of Division is committed a) when
one reasons mistakenly from the attributes of a whole to the attributes of
one of its parts, or b) when one reasons mistakenly from the attributes of a
totality of some collection of entities to the attributes of the individual
entities within that collection.
Example: Smith College is a very wealthy college. I’m dating a girl from
Smith, so she must be very wealthy.
These17informalfallaciesdonotexhaustthelistof recorded fallacy types.
They are simply the most common. Other texts use subtle variations of
these with different names. Some examples you will find include: ‘Red
Herring’ is kind of irrelevance fallacy that tries to throw the
listener off track by mentioning an unrelated point
“Straw-Man” deliberately misrepresents another’s views in order to
more easily refute them.
“Slippery-Slope” can be a variation of an unsupported or improbable
“false cause” fallacy.
38
“Hasty Generalization” can be either Accident/ Converse Accident
irrelevancy or Division/ Composition ambiguity in some texts (see
example above).
“Non-sequitur” (Latin: it does not follow) is a popular general expression
for ignoratio elenchi(see example above).
“Euphemisms” substitute “pleasant” language to refer to something
“‘unpleasant”.
“Dysphemisms” substitute unpleasant language to refer to something that
is pleasant.
Example: He’s not stupid, mom. He’s just ‘special’.
“Tu Quoque” is another variation of the ad hominem fallacy. Tu quoque
(Latin: you too) is the fallacious attack on a person because they may be
guilty of the very thing they accuse others of doing or saying.
Example: You’re a fine one to preach to me on the evils of my drug
addiction when you got hammered every night yourself when you were
my age.
39
Section 7
40
Part One Reasoning: Learning Review
Ok, what have you learned? All of these informal fallacies echo off the
walls of your daily conversations, observations, and your very own
thinking. Now you can appreciate the true significance of the title of this
book. Reviewing informal fallacies makes us realize just how easy it is to
be fooled by simple mistakes in the process of reasoning. Good reasoning
is the exception and not the rule in ordinary life, even your own. Now that
you’re determined to be a critical thinker let’s review where you are.
Reasoning or “critical thinking” is the mental discipline of
identifying, analyzing, evaluating, constructing, and refuting both
informal and formal written and oral arguments based on documented,
verifiable proof regardless of topic. Reasoning is, therefore, the process
of arriving at valid deductive arguments and/or cogent inductive
arguments in spoken or written debate.
Reasoning proficiency results in the conceptual agility to employ the
science of logic in the rigorous search for ‘best evidence’. Such
proficiency requires a creative and imaginative acuity, a blend of art and
science. It shows its highest fulfillment in the art of refutation. Achieving
this level of valid and cogent reasoning, then, requires a review of what we
have learned so far about the process of reasoning. A “learning review”
will conclude each part of this book. Serious students of reasoning will
use these learning reviews as a checklist in their notebooks or journal. In
going over this checklist students can determine for themselves if they
have sufficient knowledge of the ideas and definitions in Part One:
Reasoning to advance to the next, Part Two: Argument. This is an ideal way
to check your progress, for if you can do all these things one step at a time,
then you are well on your way to proficiency in critical thinking. If you
cannot do all these things, then you need to review Part One until you can.
Use the Twenty Reasoning Distinctions in Part One, Section 2, to sharpen
your skills in reaching these objectives.
After studying Part One: Reasoning, you should be able to:
•Recognize authentic debatable topics for informal and formal
argumentation in oral or written format.
•Understand the difference between Rhetoric and Logic in oral and
written format.
•Understand the difference between a sentence and a proposition.
41
•Recognize informal deductive and inductive arguments oral or written
format.
•Understand the difference between knowledge and belief.
•Distinguish between validity and soundness as different attributes
of arguments.
•Identify premises and conclusions in informal arguments in both oral
and written format.
•Recognize informal fallacies in everyday debate and discourse in oral
or written format.
•Understand the difference between fallacies of irrelevance,
presumption, and ambiguity.
•Understand the different roles played by explanations and
arguments in the process of reasoning.
•Develop a sense for recognizing assumptions and/or presumptions in
reasoning.
•Avoid committing informal fallacies in the process of reasoning on
debatable topics in any academic discipline.
42
Section 8
Attributes of Critical Thinkers and Writers
Accomplishing these objectives develops desirable as well as useful
attributes of the intellect. This is a good place to review a list of those
attributes found in a proficient reasoning mind of a critical thinker and
writer. Such a person is one who:
Relies on reasons instead of emotions in deciding answers to
debatable questions.
• Distinguishes truth claim statements that are matters of belief from
those that are matters of knowledge.
• Accepts the limitations of their own general background knowledge
about debatable questions.
• Separates provable truth from myth, superstition, cultural influence,
and personal prejudice.
• Understands that provable truth is a separate issue from logical validity
in deciding debatable questions.
• Establishes a clear set of analytical criteria for accepting truth claims
and arguments on debatable questions.
• Consciously recognizes their own beliefs, assumptions, presumptions,
myths, superstitions, and opinions and weighs them against provable
facts. Carefully and considerately examines the views of others on
debatable questions.
• Accepts that critical thinking is a perpetual state of self-assessment
and self discipline on debatable questions.
• Withholds judgment until all testable facts and reasonable arguments
have been considered.
• Avoids fallacies, invalid arguments, and unverifiable evidence in
examining truth claims, assumptions, and beliefs.
• Modifies their own opinions in the light of new facts and more
reasonable arguments.
• Formulates only valid deductive arguments in speaking and
writing.
• Formulates cogent inductive arguments to test for provable facts.
• Formulates counter-arguments and refutations to weak arguments.
• Formulates spoken and written arguments free of ambiguity,
presumption, and irrelevance.
• Seeks a life of ideas with others.
•
43
44
Arguments:
Deductive and Inductive
Deductive / Inductive: When it is claimed that a necessary conclusion
is drawn out of premises given as reasons to accept it, then that phase of
the reasoning process is called deductive. When a ‘probable’ or ‘likely’
conclusion is projected from verification of instances cited, then that
phase of the reasoning process is called inductive. Inductive probability
can range anywhere from ‘weak’ to ‘strong’.
Using number 15 of our Twenty Distinctions for Critical Thinkers as a start
point we notice a fundamental difference between deductive inferences and
inductive inferences in argument. Deductive inferences are arrived at out
of logical necessity called ‘entailment’. Inductive inferences on the
contrary are arrived at based on some degree of likelihood called
‘probability’. To recognize this is to acquire the mental skill in discerning
deductive from inductive arguments. Astonishingly, many well educated
people lack this mental skill. Yet a simple focus on this distinction makes the
discernment easy. Here’s how. When this inference happens out of logical
necessity in a deductive argument, then the premises are said to entail the
conclusion and the argument is valid. If the inference fails, for whatever
reason, to entail the conclusion by logical necessity, then the deductive
argument is invalid. There is no middle ground on this point. A deductive
argument is either valid or invalid. Just as no female can be ‘partially’
pregnant, so too, no deductive argument can be ‘partially’ valid. Like the
game of horseshoes you don’t get points for ‘almost’. It’s all or nothing
when it comes to the validity of deductive arguments. This logical
principle is violated in popular speech and writing quite often. We hear,
and read aberrations such as, “Her argument is more valid than any of the
others,’ or ‘He made a valid point.’ Such usage, however popular, indicates
a lack of formal training in reasoning and argument.
Such is not the case with inductive arguments. Unlike deductive
arguments, inductive arguments rely on a different sort of inference that
has nothing to do with necessary entailment. Inductive arguments rely on
the theory of probability for their strength. A strong inductive argument
relies on a strong probability. To the degree that inductive arguments lack
that strength is the degree to which they fall form strong to weak to
45
almost worthless.
Serious students of argumentation can save themselves much confusion by
only using the terms ‘valid’ and ‘invalid’ when referring to deductive
arguments. They can also distinguish themselves as well educated
individuals if they refer to inductive arguments ranking somewhere from
of most improbable to most probable. It is also apparent after our study of
Part One that validity cannot possibly apply to inductive arguments for the
simple reason that inductive arguments do not arrive at their conclusion
through the logical necessity of ‘entailment.’ They only promise a
‘probability’ for the conclusion. We will consider the nature of inductive
arguments here in Part Two: Argument, and in Part Three: Refutation.
It is sufficient to state here that premises for deductive arguments often
arise from inductive reasoning about the ‘probable’ or ‘likely’ truth of
those premises. For practical purposes there is a limit to the number of
times that one can perform an inductive observation. Sufficient numbers
of inductive instances lead ultimately to a hypothesis often stated as All X
are Y, No X is Y, Some X is Y Some X is not Y. As we shall see, these are
the building blocks of categorical syllogistic reasoning.
A reciprocal relationship then exists between deductive and inductive
arguments. The premises of deductive arguments are subject to inductive
verification. That relationship will become more apparent in this section,
as we continue through deductive arguments used in Categorical Logic,
also known as Aristotelian Logic, and then to Induction and Propositional
Logic at the end of Part Two. This basic training in the reciprocity between
deductive and inductive reasoning will enhance your critical thinking skills
for Part Three and the ‘crown jewel’ of rational thought, i.e., refutation.
First, we consider a very brief history of Categorical Logic starting with
understanding the nature of a ‘categorical reasoning’. This brief history will
help us understand the nature of a categorical ‘term’, a categorical
‘proposition’. This will prepare us to then understand the structure and
function of a categorical ‘syllogism’. Then we can learn how to build
Categorical Syllogisms to produce valid argument structures on any
topic in any academic discipline.
46
47
Part Two: Argue
48
Section 2 Categorical Logic
Aristotle (384-322 B.C.) did not invent the science of logic. He did not
even discover its basic laws, principles, ideas, or methods. But Aristotle’s
name is forever associated with the oldest and most influential system of
logic used in western culture for over 2,000 years. Why? Aristotle
codified logic from the knowledge of those who went before him.
Entering Plato’s (427-347 B.C.) Academy at the age of 17, Aristotle not
only conceptually equaled his master, but eclipsed him in the codification
of entire systems of thought including logic. As the foremost student of
the Academy, Aristotle had access to the writings, teaching, and
conceptual development of all the leading mathematics and philosophy
prior to his time. Yet all this ancient knowledge and development of
logical reasoning through formal mathematical systems was scattered
throughout prior works. Aristotle surveyed and codified these into a series
of six tracts which ancient and medieval commentators called the
Organon, now understood as Categorical Logic. In these tracts Aristotle
brought together all the reasoning insights from Thales (c.630c.550),
Pythagoras (c.569) Anaximenes, (fl. c.546), Anaxagoras
(c.500-c.428), Zeno (c.490-c.430), and Democritus (c.460-370), together
with the teachings of his mentor Plato, and his contemporary, Heraclitus
(c. 390c.322).
The six Aristotelian tracts comprising The Organon are separately titled:
Interpretation
Categories Topics
Prior Analytics Posterior Analytics
On Sophistical Refutations
Taken together, the collection was a driving force, not only for Euclid
(c. 295), and Archimedes (287212), but for the entire history of
philosophy and mathematics in western civilization till the early 1900’s.
This extraordinary influence justifies our thorough study of Aristotelian
logic.
Thanks to the Internet Classics Archive, diligent
49
Student can read English translations of these primary sources online @
http://classics.mit.edu/Browse/index.html.
Realizing that logic is the science of reasoning, Aristotle laid out his
logical principles scientifically, as he did in so many other sciences.
As is our custom, we begin this section with a few simple but precise
definitions necessary to read and understand what follows in our study
of argumentation.
Categorical Term: any term that refers to a set or class of things, real or
imaginary, that share unique, identifying attributes distinguishing
members of that set or class from members of all other sets or classes.
We call these attributes ‘class defining’ attributes.
Example: The category ‘mammal’ is distinctly identified by the attribute
‘animals that breast feed their young’. (See the literal the meaning of the
term ‘mammalian glands’)
Categorical Logic: any study of necessary inferences infer-rules, forms,
and principles between propositions that relate two classes or sets and their
members, known as categories.
Example:
No foods served at ‘Mom’s’ are greasy meals. Some pizzas are greasy
meals.
Some foods served at ‘Mom’s’ are not pizzas.
Standard Form Categorical Propositions: a n y proposition used in
Categorical Logic having only five elements expressing:
Quantity = All or only some category members
Quality = Affirmative or negative truth claim Copula = Some form of the
verb ‘to be’
Subject term = Categorical term before the copula
Predicate term = Categorical term after the copula
Examples:
All animals are mammals
Some animals are mammals
No animals are mammals
50
Some animals are not mammals
Syllogism: any two premises, single conclusion, deductive
argument.
Example: If win the Mega Lotto, then I’m rich. I win the Mega Lotto.
Therefore, I’m rich.
Standard From Categorical Syllogism: any two premise, single
conclusion, deductive argument where all the propositions are standard
form categorical propositions.
Example: All Mega Lotto winners are rich people. No poor people are
rich people.
Therefore, no poor people are Mega Lotto winners.
Contraries: Two propositions are contraries if both of them cannot be
true at the same time, but both can be false at the same time.
Example: Consider two propositions,
All psychiatrists are insane people
(and)
No psychiatrists are insane people.
Obviously, both of these claims cannot be true at the same time.
However, it may be the case that both of them are false at the same time
since it may be the case that:
Some psychiatrists are not insane people. (or) Some psychiatrists
are insane people.
Contradictories: Two propositions are contradictories if both cannot be
true, and both cannot be false at the same time.
Example: consider these two propositions:
All psychiatrists are insane people.
(and)
Some psychiatrists are not insane people.
Obviously, the truth or falsity of one entails the truth or falsity of the
51
other. They cannot both be true, and they cannot both be false because
one is the negation of the other.
Universal Affirmative Categorical Propositions: any proposition that
claims something about ALL members of a category. (See examples
above.)
Universal Negative Categorical Propositions: any proposition that
denies something about ALL members of a category. (See examples
above.)
Particular Affirmative Categorical Propositions: any proposition that
claims something about only SOME members of a category. (See
examples above.)
Particular Negative Categorical Propositions: any proposition that
denies something about only SOME members of an entire category. (See
examples above.)
In even simpler terms, while there are many members of the category
‘animal,’ only some of them are mammals, and all of those some share the
unique attribute of breast feeding their offspring. In other words, not all
animals are mammals, only some are.
In logic the word some means ‘at least one’, and the word all means
‘every one without exception.’ This is an important fact for beginning
Categorical Logic students to fully understand. Certainly there are other
words used in other systems of logic and reasoning to express partial
membership in a category, class or set, but these words are easily
translated into all, some, or none.
Examples:
‘Most’ translates to some in Categorical Logic since it does not mean all.
The same is true for expressions such as: ‘nearly all’, ‘the majority of
all’, ‘practically all’, ‘almost all’, ‘not all’, etc. For the logician, all of
these terms are synonymous with SOME.
Likewise, expressions such as ‘entire,’ ‘complete,’ ‘total,’ ‘every,’ and
‘whole,’ etc., are synonymous with ALL.
52
Why this is an important fact to absorb in understanding how logic is
the science of reasoning will become apparent as we examine the exact
logical implications of category defining attributes in Categorical Logic.
It is sufficient to note that there can be no strict ‘entailment,’ no ‘logical
necessity,’ without clear, precise, and exact meanings of the universal
term all, and the particular term some when composing propositions
about members of class, sets, or categories. A claim about ‘most’ is not a
claim about ‘all’. We hear claims on important matters everyday that
illustrate this important logical distinction. For example, is it the case that
‘most’ global warming is caused by human technology or is it the case
that ‘all’ global warming is caused by human technology? Arguments
that claim ‘all’ have a high burden of proof. A single exception can
weaken such an argument. Conversely, an argument claiming ‘some’ can
mean anything from one to ‘almost all’. Which is it? Which argument
form do we have sufficient evidence to claim? Will we be easily refuted
if we choose the argument form with insufficient evidence? We tackle
that problem in Part Three: Refutation.
From these simple observations, and definitions we are now ready to
advance our understanding of categorical argumentation. We next study
how Aristotle constructs his entire logic system from just four basic kinds
of propositions about categories, their members, and the logical inferences
that can be reasoned between them. In so doing, we take up the study of a
practice of argumentation that has been analyzed, tested, proven, and
endured in western culture for nearly two thousand years.
Now that we generally understand the basic ideas of a categorical, term,
a categorical proposition, and the idea of a categorical syllogism used in
Categorical Logic we can proceed to the necessary inferences that can
be made from categorical propositions.
As we will see in the next section, a necessary inference is a step from
one idea to another idea without any intermediary idea being necessary to
make that step.
53
Section 3
Categorical Propositions
Not all sentences are propositions. However, every sentence or sentence
fragment that states a claim is a proposition. However, only some
propositions are categorical. Aristotle observed that all categorical
propositions can be reduced to just four types, divided by only two
elements: Quantity (number, all or some), and Quality (affirmative or
negative). From these divisions Aristotle generated the four basic types of
categorical propositions that are the foundation for his entire logic system.
Simply using the two categories of animals and humans, here are those
four basic categorical propositional types.
Universal affirmative:
All animals are mammals
Particular affirmative:
Some animals are mammals
Universal negative:
No animals are mammals
Particular negative: Some animals are not mammals
These four categorical proposition Types exhaust all logically
possible relations between members of these two (or any) categories,
as Aristotle reasoned. Alert students will notice immediately that only
two of these four categorical propositions are true, based on scientific
observations of animals and mammals:
Some animals are mammals (particular affirmative) Some animals are not
mammals (particular negative)
The other two, the universal affirmative and the universal negative, we
know are false from scientific observations. A categorical proposition,
then, affirms or negates, in whole or in part (all or some), that members
of one category are included or excluded as members of another
category. Aristotle identified each of these propositional Types as the four
most basic in categorical reasoning. It is believed that medieval scholars
assigned the letters A, E, I, or O to these four Types from the Latin words
AffIrmo meaning to affirm, and NEgO meaning to negate.
Type A. universal affirmative proposition states that every member of
one class is also a member of the second class.
54
55
Example: All humans are mortal animals.
Type E. universal negative proposition states that no member of one
class is also a member of the second.
Example: No humans are mortal animals.
Type I. particular affirmative proposition states that some members of
one class are members of the second.
Example: Some humans are mortal animals.
Type O. particular negative proposition states that some members of
one class are not members of the second.
Example: Some humans are not mortal animals.
The concept that members of one category are included or excluded by
all or some members of another category is called distribution. This
notion of distribution is the most essential power in Categorical
(Aristotelian) Logic; in fact, it is the very analytic power of deductive
validity itself. Distribution may be seen then as the very engine of
logical entailment, and it rests on just three fundamental Laws of
Thought. Here is Aristotle's formulation.
The Law of Identity
A thing is what it is. A = A
The Law of Non-Contradiction
A thing cannot be and not be at the same time and in the same respect. A
does not equal not A
The Law of Excluded Middle
A thing either is or it is not.
Between A and not A there is no middle term
Applied to truth claim propositions:
Law of identity = A is A This tautology (a statement equivalent to itself)
forms the basis for all logic.
Law of non-contradiction = Nothing can be itself and not be itself at the
same time in exactly the same sense: A is., and not A is not cannot both
be true at the same time. Or in Aristotle’s words, one cannot say of
something that it is, and that it is not in the same respect, and at the
same time.
Law of the excluded middle: For any proposition either that proposition
is true or its negation is true. Between A and/or not A there is no third
possibility. It is not logically possible that there should be anything
56
between the two parts of a contradiction.
Given the nature of philosophical inquiry it’s not surprising that
many attempts have been made to refute these three Laws of Thought
without invoking them in the very act of arguing against them. Aristotle
himself is thought to have placed some limits on the laws of thought
that he codified from earlier thinkers like Parmenides. Clearly a thing
cannot be both ‘green’ and ‘not green’ at the same time and in the
same respect. But this may be attributable more to the construct of
human perception than to the world of ‘green’ or ‘not green’ things.
“The same attribute cannot at the same time belong and not belong
to the same subject and in the same respect.”
(Metaphysics G, 3,1005b18-20)
Aristotle seems to warn against imposing the three laws of thought that
order thinking on the natural world of things, events and their attributes.
So the debate goes. For our purpose, there is little or no debate about
the irrefutability of these three laws without involving a contradiction.
That of course does not mean there is no sound refutation of these three
laws. It just makes it virtually impossible to imagine how such a
refutation could be construed without employing them
Since the first law, the law of identity is a tautology, i.e., a statement
equivalent to itself; it is not arguable without uttering an absurdity.
The second, the law of non-contradiction, is also unarguable
without actually using the law itself to refute it. To do so is to present
a contradiction resulting in yet another absurdity. One cannot prove it
either without begging-the-question.
As for the third, the law of the excluded middle, it follows necessarily
from the first two. For if everything that is, is, and if it cannot both be
the case that something is, and that something is not, then it follows of
necessity that between A is, and A is not, no logical middle option is
possible. Therefore, to master classical deductive logic, the following
precise definition must be fully understood. This definition is precise in
the sense that it tells us exactly what distribution is, and precisely what it
is not. A categorical term is distributed if, and only if, the categorical
proposition that contains it tells us something about ALL members of
57
that categorical term. Conversely, a categorical term is undistributed if,
and only if, the categorical proposition that contains it does NOT tell us
something about ALL members of that categorical term.
You will want to commit this definition to memory. You will
apply it constantly in your full understanding of categorical
argumentation. As previously stipulated, Categorical Propositions are
said to have quality (either affirmative or negative), and quantity
(either universal or particular) and that they have distributed and/or
undistributed categorical terms. Again, a proposition is said to
distribute a term if that proposition refers to all members of the class
designated by the term. The following chart illuminates the ways in
which A, E, I, and O type propositions either distribute, or do not
distribute their subject and/or predicate terms. You should also commit
this chart to memory as a visual companion to your working definition
of distribution.
Quantity & Quality
Type
Standard From
Distribution of Terms
A
All S is P
Universal Affirmative
E
No S is P
Universal
Negative
I
Some S is P
Particular Affirmative
Neither Subject nor Predicate
distributed
O
Some S is not P
Particular Negative
Only Predicate distributed
Subject distributed
Predicate not distributed
Both Subject and Predicate
distributed
The reason for the emphasis on Predicate term is distributed for Type
O categorical propositions is because most students fail to see why
this is the case. How does a proposition like, Some pizzas are NOT
greasy things, tell us something about ALL greasy things? The answer
is simple to understand if you read the proposition in its full logical
exactitude. Some pizzas are not greasy things. Literally means in logic:
There exists at least one thing called a pizza, and that one thing called
a pizza is not included in
the entire category of greasy things. So, in logical terms, all Type O
categorical propositions do in fact distribute the predicate term. This is
another vital point to grasp. Using these four basic Types of
categorical propositions, Aristotle is able to construct a square to
graphically illustrate the several ways these propositions can be opposed
to one another. The traditional square of opposition, shown below,
58
graphically displays the opposing relationships that exist between the four
different categorical proposition types.
When S and P are used for subject and predicate terms in the
propositions, they are said to be opposed to each other in any of six
ways:
1.
2.
3.
4.
5.
6.
All S is P, and Some S is not P are contradictories.
No S is P, and Some S is P are contradictories.
All S is P, and No S is P are contraries.
Some S is P, and Some S is not P are subcontraries
Some S is P, is the subaltern of All S is P
Some S is not , is the subaltern of No S is P
Opposition by propositional Type yields:
Types A and E are contraries
Types I and O are subcontraries
Types A and O are contradictories
Types E and I are contradictories
Type I is the subaltern of Type I
Type O is the subaltern of Type E
(Note: The modern interpretation of the traditional Aristotelian Square
of Opposition only recognizes Contradictions as being opposed to each in
the strictest logical sense. This is so because Contrary propositions A &
E can both be false at the same time and Subcontrary propositions I and
O can both be true at the same time thus they are not strictly opposed to
each other as contradictions are except under very limited conditions.
59
Now we are ready to make sense of the graphic below depicting the
Traditional (Aristotelian) Square of Opposition for all four Types of
Standard Form Categorical Propositions.
As noted, you may find that the square of opposition in some
contemporary logic texts appears quite different. While contradictories
are accepted by most modern logicians, contraries, subcontraries and
subalterns are not. In modern logic text books, the traditional square of
opposition is reduced to something like the following diagram. Why is
this?
The answer revolves around the philosophical debate among modern
logicians about the very nature of Categorical Terms, and the Universal
and Particular Categorical Propositions that relate them. Simply stated, if
all categorical terms were to refer to classes, sets, or categories of
members that actually exist, then there would be no debate about the
existential import of such terms and their propositions. Modern logicians
debate this existential import question. While our concern as critical
60
thinkers is not the same as that of the professional logician, nevertheless
the point does need clarification. In mathematics, literature, and even
science, we often refer to sets, classes, and categories of things that are
purely imaginary or theoretical. The empty set in mathematics, the unicorn
in literature, the black hole in astrophysics, the string of contemporary
physics; these, and many others, are examples of categories that we
imagine to have members, yet lack direct experience that such things
actually exist. Are we then prevented from using categorical logic to
reason about these empty categories? Certainly we are not.
There is a simple and effective way to rescue the traditional square of
opposition from this criticism of modern logicians. We just stipulate,
when referring to any category, that we refer to things either real or
imagined. As we will be see in the section on Definitions, in Part Three:
Refutation to ‘stipulate’ simply means to ‘accept as agreed’. Opposing
lawyers in court often stipulate to facts of the case at trial. Mathematicians
stipulate sets with no members to work out proofs. Writers stipulate
imaginary worlds and creatures in their poems and novels. Scientists
stipulate hypothetical laws, principles, forces, powers, and substances
when endeavoring to explain events which elude existing theories.
Applying the three basic laws of thought, then, to sets, classes, and
categories with no members is not hindered. We can continue to reason
through categorical arguments provided we stipulate that if categorical
terms had any members, even hypothetical ones, then the principles of
categorical logic apply. We adopt this stipulation here.
Three more ideas are introduced in this section to complete our
understanding of the power in categorical propositions around the square
of opposition. These ideas are; conversion, obversion and contraposition.
Each are instances of immediate inferences.
An immediate inference is a necessary mental progression from one
proposition to another without any other proposition being needed in
the process.
Example: If any Type A proposition is factually true, then its
contradictory Type O proposition must be factually false by immediate
inference.
Two useful and often used instances of immediate inference in
61
categorical logic are conversion and obversion. Contraposition is of
interest to those with a fondness for logical structures but is seldom used
in ordinary discourse. Nevertheless, it is introduced here for
completeness of immediate inferences that can be drawn, in some
instances, from A E I and O categorical propositions.
Conversion: swapping the position of the subject and predicate terms in
any standard form categorical proposition. (Valid immediate inference
only for Type E and Type I categorical propositions)
Examples:
No S is P converts to No P is S
Some S is P converts to Some P is S
Obversion: changing the Quality of the proposition, and replacing the
predicate term with its complement (everything other than that term
signified by placing non before that term).Obversion is a valid immediate
inference for all Type A, E, I, and O categorical propositions.
Examples:
A All S is P. obverts to Type E No S is not-P. E No S is P. obverts to
Type A All S is not P.
I Some S is P obverts t0 Type 0 Some S is not not-P 0 Some S is not P.
obverts to Type I Some S is not-P.
The reason we would want to convert and/or obvert any standard form
categorical proposition is to observe if an immediate inference can be
validly derived from the outcome. When we walk around the square of
opposition, applying conversion to each of the propositional types (A, E,
I, & O), we discover something very interesting. We learn that, while
conversion of a Type A and Type O proposition does not produce
reciprocally true/false results, conversion of Type E and Type I
propositions does in fact produce reciprocally true/false results.
Examples:
All S is P does not entail that All P is S by conversion immediate
inference.
62
Some S is not P does not entail that Some P is not S by conversion
immediate inference.
But
No S is P does entail that No P is S by conversion immediate inference.
And
Some S is P does entail that Some P is S by conversion immediate
inference.
You may have noticed quickly that Type E propositions distribute
both subject and predicate terms, while Type I propositions distribute
neither subject nor predicate term. The reason lies in the very precise
definition we previously gave for the term distribution. Ordinary
language examples, then, show the obverse of ‘All ants are insects’ is
‘No ants are noninsects’; the obverse of ‘No fish are mammals’ is ‘All
fish are nonmammals’; the obverse of ‘some musicians’ are males is
‘some musicians are not nonmales’; and the obverse of ‘some cars are not
sedans’ is ‘some cars are nonsedans’. In this way, obverting a
proposition gives us a logical equivalent of the original proposition
before obversion is performed. Obversion is the only immediate
inference that is valid for all four categorical propositions, Types, A, E,
I, and O.
In each of the instances cited above, the original proposition and its
obverse will have exactly the same truth value regardless if it turns out to
be true or false. Not only do the immediate inferences provided by
conversion and obversion serve our understanding of the notion of
distribution in categorical logic, they are useful in developing our
refutation skills, as presented in Part Three. They reveal logical
exactitude. For instance, just because someone is a nonhero, that
someone is not necessarily a coward. Knowledge of obversion reveals
this exact meaning. Equally useful is the understanding by conversion
that while it may be the case that, All democratic ideals are ideals
good for corporations, it does not follow that, All ideals good for
corporations are good for democratic ideals.
Contraposition: is formed as a combination of conversion and
63
obversion. To form the contrapositive of a categorical proposition these
steps are taken;
•
Switching the subject and predicate terms, as in taking the converse
Replacing both the subject and the predicate terms with their
complements
•
•
The quality and quantity of the proposition remain as they were.
It is always valid to infer the contrapositive of an A proposition. An
A proposition says that the class of S is included within the class of P.
So anything outside the class of P (i.e., all the non-P) must be outside
the class of S (i.e., it must be a non-S).
Example:
Boston is in America, so if you're not in America, you're not in Boston.
While being in America is a necessary condition for being in Boston it is
not a sufficient condition.
Contraposition is not a valid immediate inference for I and E
propositions.
Examples:
The E proposition, "No primate is an aquatic animal," is clearly not
equivalent to its contrapositive, "No nonaquatic animal is a
nonprimate," because the first is true and the second false (cows are
nonaquatic animals but they are nonprimates). Similarly, the I
proposition, "Some soldiers are nonofficers," is clearly not equivalent
to its contrapositive, "Some officers are nonsoldiers."
Besides the type A proposition the type O proposition is the only other
type that is equivalent to its contrapositive.
The true value of mastering these immediate inferences is knowing how
and when they fail validity. The art of refutation presented in Part
Three here will demonstrate the usefulness of pointing out that just
because a person is not a hero that does not entail by immediate
inference that the person is a coward. Yet this false inference is very
often made in popular speech. However, before we can refute arguments
we must first build them. We must learn their form and their structure.
Following this is the formal study of the most powerful form of
64
argument, the categorical syllogism.
65
Section 4
Categorical Syllogisms
The categorical syllogism is a very simple form of argument. It
harnesses the ‘power of distribution’ to generate a conclusion from only
two categorical premises with absolutely certain validity because the
‘form’ of the four types of categorical propositions, A, E, I, & O, express
either category inclusion or exclusion of members in one class with
members of another class. Utilizing the power of distribution is precisely
what happens in the argument structure known as a Standard Form
Categorical Syllogism.
‘Validity’ then, is un...
Purchase answer to see full
attachment